Name:____________________________________ Date:___________ Period:___________ Score:_________
Isometric Transformations: Rotations
Rotation: A transformation that turns the plane through a given angle about (around) a given
point.
In other words, a translation is a turn around a center point. The angle is called the angle of
rotation and the point around which the plane is turned is called the center point of rotation.
But before we start spinning around, lets talk about angles and clocks.
1. What kind of angle is this?
2.
What kind of angle is this?
How many degrees does
it measure?
How many degrees does it measure?
3. How many degrees are there in a quarter
rotation clockwise?
4. How many degrees are there in a quarter
rotation counter-clockwise?
Did this rotate the same
direction as a clock or against it?
Did this rotate the same
direction as a clock or against it?
So a rotation counter-clockwise means rotate
So a rotation counter-clockwise means rotate
_____________________________ a clock.
We can also say this is a -90° rotation.
_____________________________ a clock.
We can also say this is a 90° rotation.
5. How many degrees are there in a half
rotation counter-clockwise?
6. How many degrees are there in a half
rotation clockwise?
Did this rotate the same
direction as a clock or against it?
Did this rotate the same
direction as a clock or against it?
So a rotation counter-clockwise means rotate
So a rotation counter-clockwise means rotate
_____________________________ a clock.
We can also say this is a 180° rotation.
_____________________________ a clock.
We can also say this is a -180° rotation.
1
© 2014 LetsPracticeGeometry.com
Name:____________________________________ Date:___________ Period:___________ Score:_________
Directions: Use patty paper, Geometry software, or any other method available to you to
rotate each figure as directed. Make sure to label your new figure.
1. Rotate ABC 90° clockwise about the origin.
2. Rotate ABC 90° counter-clockwise about the
origin. RO,90°
RO,-90°
B
B
A
A
C
C
3. Rotate ABC 180° clockwise about the origin. 4. Rotate ABC 180° counter-clockwise about
RO,-180°
the origin. RO,180°
B
A
B
A
C
5a. What do you think happens to the center
point of rotation? Does it move?
C
6. Is a rotation an isometric transformation?
b. What do think… is each points in image the
same distance from the center as in the
original figure? Why?
2
© 2014 LetsPracticeGeometry.com
Name:____________________________________ Date:___________ Period:___________ Score:_________
Directions: Use patty paper, Geometry software, or any other method to rotate each figure as
directed. Make sure to label your image figure correctly.
1. Rotate BUG 180° clockwise about the origin. 2. Rotate CHEF 180° counter-clockwise about
RO,-180°
the origin. RO,180°
B
G
U
H
C
F
E
3. Rotate BACH 90° clockwise about the origin. 4. Rotate ABCDE 90° counter clockwise about
RO,-90°
the origin. RO,90°
B
A
C
H
A
B
C
E
5. Rotate TOE 90° clockwise about the origin.
D
6 Rotate DAY 90° counter- clockwise about the
origin. RO,90°
RO,-90°
A
D
T
Y
O
E
3
© 2014 LetsPracticeGeometry.com
Name:____________________________________ Date:___________ Period:___________ Score:_________
Directions: Refer to some of the problems on the previous page to help you make conjectures
about the functions of rotations about the origin.
8. For problem 5 (90° rotation clockwise)…
7. For problem 1 (180° rotation clockwise)…
What are the coordinates of the vertices of the What are the coordinates of the vertices of the
original figure?
original figure?
B (___,___) U (___,___) G (___,___)
T (___,___) O (___,___) E (___,___)
What are the coordinates in its image?
What are the coordinates in its image?
B’ (___,___) U’ (___,___) G’ (___,___)
T’ (___,___) O’ (___,___) E’ (___,___)
Describe the relationship between the original
an image coordinates in words.
Describe the relationship between the original
an image coordinates in words.
Describe the relationship with a function.
Describe the relationship with a function.
(x,y) → (___________, ___________)
(x,y) → (___________, ___________)
9. For problem 5 (90° rotation counter
clockwise)…
10. Bill says if you rotate a figure 180
clockwise or counterclockwise you will get the
same image. Sally says you won’t. Who is
What are the coordinates of the vertices of the correct? Why?
original figure?
D (___,___) A (___,___) Y (___,___)
What are the coordinates in its image?
D’ (___,___) A’ (___,___) Y’ (___,___)
Describe the relationship between the original
an image coordinates in words.
Describe the relationship with a function.
(x,y) → (___________, ___________)
4
© 2014 LetsPracticeGeometry.com
Name:____________________________________ Date:___________ Period:___________ Score:_________
Directions: We can also rotate figures around other points. Use patty paper, Geometry
software, or any other method to rotate each figure as directed. Make sure to label figure.
1. Rotate COW 180° clockwise about point P.
2. Rotate CAR 90° counter-clockwise about
point S. RS,90°
Rp,-180°
C
W
O
P
S
A
C
3. Rotate BIKE 90° counter-clockwise about
the point K. RK,90°
R
4. Rotate ABC 90° clockwise about point E.
RE,-90°
B
A
E
B
I
K
E
D
C
5. Rotate ABC 180° counter-clockwise about
point Y. RY,180°
W
6. Rotate PIN 90° clockwise about point R.
RR,-90°
X
P
Z
Y
R
N
5
I
© 2014 LetsPracticeGeometry.com